Psi4
fd_geoms_freq_0.cc File Reference

fd_geoms_freq_0(): returns geometries necessary for finite-difference computation of second derivatives from energies; puts undisplaced geometry last in list More...

`#include "findif.h"`
`#include "psi4/liboptions/liboptions_python.h"`
`#include "psi4/libpsi4util/PsiOutStream.h"`
`#include "psi4/libmints/matrix.h"`
`#include "psi4/libmints/molecule.h"`
`#include "psi4/libmints/cdsalclist.h"`

## Namespaces

psi
This is all defined in python.cc initialize.

psi::findif

## Functions

std::vector< SharedMatrix > psi::findif::fd_geoms_freq_0 (std::shared_ptr< Molecule >, Options &, int irrep=-1)

## Detailed Description

fd_geoms_freq_0(): returns geometries necessary for finite-difference computation of second derivatives from energies; puts undisplaced geometry last in list

Finite-difference formulas 3-point - diagonal O(1/h^2): [f(1,0) + f(-1,0) - 2f(0,0)]/(h^2) [which is same as : [f(2,0) + f(-2,0) - 2f(0,0)]/(4h^2) 3-point - off-diagonal O(1/h^2): new-way: [f(1,1)+f(-1,-1)+2f(0,0) -f(1,0) -f(-1,0) -f(0,1) -f(0,-1)]/(2h^2)

5-point formula - diagonal O(1/h^4): [-f(-2,0) + 16f(-1,0) + 16f(1,0) - f(2,0) - 30f(0,0)] / (12h^2) 5-point formula - off-diagonal O(1/h^4): [-1f(-1,-2) - 1f(-2,-1) + 9f(-1,-1) - 1f(+1,-1)

• 1f(-1,1) + 9f(+1,+1) - 1f(+2,+1) - 1f(1,2)
• 1f(-2,0) - 7f(-1,0) - 7f(+1,0) + 1f(+2,0)
• 1f(0,-2) - 7f(0,-1) - 7f(0,+1) + 1f(0,+2) + 12f(0,0)]/(12h^2)